Find the equation of a line passing through the point (-4,1) and perpendicular to theline 3y = 12x - 9.
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Answer:
A. y=-1/4x
Step-by-step explanation:
We have the information 3y=12x-9, the lines are perpendicular, and the new line passes through (-4,1). First, you want to put the original equation into slope intercept form by isolating the y, to do this we need to divide everything by 3 to get y=4x-3. The slopes of perpendicular lines are negative reciprocals so you need to find the negative reciprocal of 4, so flip it to 1/4 and multiply by -1, we get the slope of the new line as -1/4. So far we have the equation y=-1/4x+b. We are given a point on the line, (-4,1), we can plug these into the equation as x and y to solve for the y-intercept, b. You set it up as 1=-1/4(-4)+b. First you multiply to get 1=1+b, then you subtract 1 from both sides to isolate the variable and you get b=0. Then you can use b to complete your equation with y=-1/4x, or letter A.
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Which of the following is equivalent to 46? 6 + 6 + 6 + 6 4 • 4 • 4 • 4 • 4 • 4 4 + 4 + 4 + 4 + 4 + 4 6 • 6 • 6 • 6
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Answer:
Management Farming Construction
Step-by-step explanation:
Enter your answer in the box.
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Hey, this is worked out the same way as the last problem you posted!
Remember that constant of proportionality is slope...
(y2-y1) ÷ (x2 -x1)
↓
(225 - 135) ÷ (5 - 3)
↓
90 ÷ 2
↓
45
The constant of proportionality is 45
Do not do any rounding.
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Givens
Slower car
r = r
t = 12 hours
d = ?
Faster car
r = r + 20
t = 8 hours
d = ?
It doesn't matter what the exact distance is. You just have to know that the 2 distances are equal ie going to the mountains from his home is the same distance as going from the mountains to his home.
d = r * t
r * 12 hours = (r + 20)* 8 hours. Remove the brackets on the right
r*12 = 8r + 20*8
r*12 = 8*r + 160
r*12 - 8r = 8r - 8r + 160
4r = 160
r = 40 miles / hour
=================
Slower Ride determines the distance.
d = r*t
d = 40 * 12
d = 480
Check
Use the faster rate (r + 20) = 40 + 20 = 60 mph
60 * 8 = 480. Both distances work out to be the same.
Grove for 40 minutes, how far did she travel? (1 hour = 60 minutes)
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Answer: 30 miles